Question

a convex hexagon has exterior angles that measure 48,52,55,62,and 68. what is the measure of the exterior angle of the sixth vertex?

Answer 1

Answer:

this is very easy answer

Answer 2

Given:

Exterior angles of a convex hexagon=48°, 52°, 55°, 62°, 68°

To find:

The measure of the exterior angle of the sixth vertex

Solution:

The measure of the exterior angle of the sixth vertex is 75°.

We can find the measure by following the given steps-

We know that the sum of all the exterior angles of any convex polygon is 360°.

So, the sum of all the exterior angles of the given hexagon=360°

We are given that the convex hexagon has the following exterior angles of its 5 vertices-

48°, 52°, 55°, 62°, 68°

Let us assume that the sixth exterior angle is X.

Now, the sum of all the exterior angles=48+ 52+ 55+ 62+ 68+X

48°+ 52°+ 55°+ 62°+ 68°+X=360°

285°+X=360°

X=360°-285°

X=75°

The sixth exterior angle measures 75°.

Therefore, the measure of the exterior angle of the sixth vertex is 75°.